Find the linearization of the following curves at a suitably chosen integer near a

Question

Find the linearization of the following curves at a suitably chosen integer near a
$f(x) = x^2 + 2x$

$a=0.1$

in this i used the formula $L(x)=f(a) + f'(a)(x-a)$ and solved and got $L(x)=2.2x-0.01$

is it right or am i misinterpreting the question?

Answer 1

$$ f(x) = x^2 + 2x $$ therefore $$ f^{'}(x)=2x+2. $$ Given a differentiable function f defined near a, the linearization of f at a is the linear function given by $L(x) = f(a) + f^{'}(a)(x − a)$.

Now we have: $$ L(x) = f(a) + f^{'}(a)(x − a)=0.21+2.2(x-0.1)=2.2\cdot{x}-0.01. $$

Yes, you are right.